scipy.sparse.linalg.bicgstab

scipy.sparse.linalg.bicgstab(A, b, x0=None, tol=1e-05, maxiter=None, M=None, callback=None, atol=None)

Use BIConjugate Gradient STABilized iteration to solve Ax = b.

Parameters

A{sparse matrix, ndarray, LinearOperator}

The real or complex N-by-N matrix of the linear system. Alternatively, A can be a linear operator which can produce Ax using, e.g., scipy.sparse.linalg.LinearOperator.

bndarray

Right hand side of the linear system. Has shape (N,) or (N,1).

Returns

xndarray

The converged solution.

infointeger

Provides convergence information:

0 : successful exit >0 : convergence to tolerance not achieved, number of iterations <0 : illegal input or breakdown

Other Parameters

x0ndarray

Starting guess for the solution.

tol, atolfloat, optional

Tolerances for convergence, norm(residual) <= max(tol*norm(b), atol). The default for atol is 'legacy', which emulates a different legacy behavior.

Warning

The default value for atol will be changed in a future release. For future compatibility, specify atol explicitly.

maxiterinteger

Maximum number of iterations. Iteration will stop after maxiter steps even if the specified tolerance has not been achieved.

M{sparse matrix, ndarray, LinearOperator}

Preconditioner for A. The preconditioner should approximate the inverse of A. Effective preconditioning dramatically improves the rate of convergence, which implies that fewer iterations are needed to reach a given error tolerance.

callbackfunction

User-supplied function to call after each iteration. It is called as callback(xk), where xk is the current solution vector.

Examples

>>> from scipy.sparse import csc_matrix
>>> from scipy.sparse.linalg import bicgstab
>>> R = np.array([[4, 2, 0, 1],
...               [3, 0, 0, 2],
...               [0, 1, 1, 1],
...               [0, 2, 1, 0]])
>>> A = csc_matrix(R)
>>> b = np.array([-1, -0.5, -1, 2])
>>> x, exit_code = bicgstab(A, b)
>>> print(exit_code)  # 0 indicates successful convergence
0
>>> np.allclose(A.dot(x), b)
True